PiHex

PiHex was a distributed computing project to calculate specific bits of Pi, the greatest calculation of Pi ever successfully attempted. 1,246 contributors used idle time slices on almost two thousand computers to make its calculations. They made use of Bellard's formula, a faster version of the BBP formula, with the algorithm discovered by Bailey, Borwein, and Plouffe in 1995.

After setting three records, calculating 76 digits past in each case (and 3 before), the five trillionth bit, the forty trillionth bit, and the quadrillionth bit, the project ended September 11, 2000.

PiHex didn't conduct their task the customary way, using the digits 0 through 9 (Base 10). Instead, they calculated Pi in binary (or Base 2, i.e., using only 0s and 1s).

Here are the final digit strings for each of the three calculations:

* Binary digits of Pi from five trillion to five trillion seventy-six (completed August 30, 1998)::00111111001000101011100110011110011000111100100001011010110110101100101111001

* Binary digits of Pi from forty trillion to forty trillion sixty-four (February 9, 1999)::00000111110011111111100110111000111010001011101011001001111100000

* Binary digits of Pi from one quadrillion to one quadrillion sixty (September 11, 2000)::0011000100001011010110000011010011100101101101100000111010011

Therefore, the smallest-value digit of Pi in binary known to man is 1 at position 1,000,000,000,000,060 (one quadrillion sixty) or 10¹⁵+60.

To calculate the five trillionth digit (and the following seventy-six digits) took 13,500 CPU hours, utilizing 25 computers from 6 different countries. The forty trillionth digit required 84,500 hours and 126 computers from 18 different countries. The highest calculation, the one quadrillionth digit, took 1.2 million computer hours and 1,734 computers from 56 different countries. Total resources: 1,885 computers in 80 unique countries donated 1,298,000 CPU hours. The average computer that was used to calculate would have taken 148 years to complete the calculations alone.

While the PiHex project calculated the highest placed (or smallest valued) digits of Pi ever attempted in any base, second place is held by Professor Yasumasa Kanada who derived the 1.2411 trillionth digit in base 10 (which is 5).

External links

* [http://oldweb.cecm.sfu.ca/projects/pihex/index.html The official PiHex site]
* [http://oldweb.cecm.sfu.ca/projects/pihex/news.html PiHex News]
* [http://oldweb.cecm.sfu.ca/projects/pihex/status.html PiHex Status]